Vanishing theorems for coherent automorphic cohomology

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Abstract

We consider the coherent cohomology of toroidal compactifications of locally symmetric varieties (such as Shimura varieties) with coefficients in the canonical and subcanonical extensions of automorphic vector bundles, and give explicit conditions for them to vanish in certain degrees. We also provide algorithms for determining all such degrees in practice.

Original languageEnglish (US)
Article number39
Number of pages43
JournalResearch in the Mathematical Sciences
Volume3
Issue number1
DOIs
StatePublished - 2016

Bibliographical note

Funding Information:
The author would like to thank Zhiwei Yun and Xinwen Zhu for their helps on understanding the conceptual meaning behind Theorem 3.8, which he initially only observed as an intriguing fact from explicit calculations. He would also like to thank Michael Harris for helpful discussions on the cohomology of Shimura varieties, and to thank Junecue Suh for sending him the preprint [44]. The author’s research was partially supported by the National Science Foundation under agreement No. DMS-1352216, and by an Alfred P. Sloan Research Fellowship. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of these organizations.

Keywords

  • Automorphic bundles
  • Canonical extensions
  • Coherent cohomology
  • Locally symmetric varieties
  • Shimura varieties
  • Toroidal compactifications
  • Vanishing theorems

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